BEVERLY HILLS, Calif./WASHINGTON (Reuters) - The U.S. House of Representatives could vote in May on a bill easing bank rules adopted after the 2007-2009 global financial crisis, a leading Republican lawmaker said on Monday.

The comments by Representative Kevin McCarthy, the House majority leader, marked the strongest sign yet a deal could soon be reached between the House and Senate to pass the first rewrite of the 2010 Dodd-Frank financial reform law.

The Senate voted 67-32 last month in favor of a bipartisan bill that would ease oversight of small and mid-sized banks.

House Republicans have stalled voting on the Senate bill on the grounds that additional provisions should be included to further lower the regulatory burden on banks and make it easier for small companies to raise capital.

Many Democrats say Dodd-Frank provides critical protections for consumers and taxpayers. While the Senate bill passed with the support of 17 moderate Democrats, key members of the party, including Senator Mark Warner, have said they would withdraw support if any further changes were made.

That has raised fears among bank lobbyists that the House could sink the bill if it refused to approve the Senate version.

But McCarthy said there was a willingness on both sides to pass the bill, which said would reform, rather than repeal, Dodd-Frank.

"I think you are within a month of getting it ... done," he told the Milken economic conference in Beverly Hills, California.

"At the end of the day, there will be a bill at the president's desk," he added, pledging to deliver legislation to President Donald Trump before congressional elections in November.

Trump said in March he would sign the bill once it had been approved by both the House and Senate

Last week, Republican Representative Jeb Hensarling, chairman of the House Financial Services Committee, said he was "certainly open to other pathways" to pass legislation aimed at helping small businesses.

McCarthy echoed these comments on Monday, suggesting some of the House's wish list could be included in separate legislation.

Speaking at the same event, U.S. Treasury Secretary Steven Mnuchin said later on Monday he was hopeful the changes, which he said were important for small lenders and community banks, would be passed soon.

"This should get done now. I am hopeful this gets done in the next 30 to 60 days," he added.

(Reporting by Lawrence Delevingne in Beverly Hills, Calif. and Katanga Johnson in Washington; Editing by Michelle Price and Peter Cooney)